Energetic Particle Reservoirs: 2. Solutions of the Transport Equation and Comparison with Data

A general solution of the energetic particle reservoir transport equation is developed using the method of characteristics for a linear (non-homogeneous) partial differential equation. In the limiting case of energy-independent particle streaming parallel to the magnetic field, the solution for non-relativistic particles depends wholly on their energy/charge. This simple prediction is consistent with the energy shifts that bring the intensity histories of solar energetic O and Fe ions into (normalized) agreement during the post-maximum phase of large SEP events, as well as the common ordering by total energy of energetic ion spectra (H, He, N, O, Ne) in the heliosheath over four orders of magnitude (40 keV-1 GeV).